Two cross roads, each of the width 10m, cut at right angles through teh centre of a
rectangle park of length 700m and breadth 300m and parallel to its sides. Find the areas of the
roads. Also find teh area of the park excluding cross roads. Give the answers in hectares?
Answers
Step-by-step explanation:
Here, PQ=10m and PS=300m, EH=10m and EF=700m
And KL=10m and KN=10m
Area of roads = Area of PQRS+Area of EFGH−Area of KLMN
[∵ KLMN is taken twice, which is to be subtracted]
=PS×PQ+EF×E−K×KN
=(30×10+(70×10−(1×10)
=300+700−100
=9900m
2
Area of road in hectares, 1m
2
=
10000
1
hectares
∴9900m
2
=
10000
9900
=0.99 hectares
Now, Area of park excluding cross roads = Area of park−Area of road
=(A×AD−9900
=(700×300)−9,900
=2,10,000−9,900
=2,00,100 m
2
=
10000
200100
hectares=20.01 hectares.
solution
Step-by-step explanation:
Length of the road parallel to the length of the park= 700m
Width of the road= 10m
Area of the road= l\times b=700m\times10m=7000m^2l×b=700m×10m=7000m
2
Length of the road parallel to the breadth of the park =300m
Width of the road= 10m
Area of this road= l\times b=300m\times10=3000m^2l×b=300m×10=3000m
2
Area of both the roads
=7000m^2+3000m^2-Area\ of\ the\ common\ portion\=7000m
2
+3000m
2
−Area of the common portion
=10000m^2-10m\times10m=10000m
2
−10m×10m
=10000m^2-100m^2=10000m
2
−100m
2
=9900m^2=0.99=9900m
2
=0.99
Area of the park = l\times bl×b
=700m\times300m=210000m^2=700m×300m=210000m
2
Area of the park excluding the roads
=210000m^2-9900m^2=210000m
2
−9900m
2
=200100m^2=20.01=200100m
2
=20.01
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